Individual and collective dynamics of contact behaviour


Sebastian Funk
18 May, 2017
SIMID Workshop

Questions

  1. What is the relative importance of individual vs collective variation in contact behaviour?
  2. How can we find out about long-term changes in collective contact behaviour

Individual vs. collective variation in contact behaviour

Longitudinal contact data

  1. There is variation in the number of contacts both within and between individuals
  2. The number of contacts is overdispersed both on the individual and the collective scales

Are there high-contact individuals or high-contact days?

  • Hierarchical model implemented in stan

(http://mc-stan.org)

  • Negative binomial model with two parameters vs negative binomial with two parameters per person, compared with Deviance Information Criterion (DIC)

Model comparison

\(\mathrm{contacts} \sim \mathrm{NegBin(\mu, k)}\)

Model Δ DIC
Collective 0
Individual -5k

Covariates

Age

Age

Household size

Urban/rural

Covariate model

\(\mathrm{contacts} \sim \mathrm{NegBin(\mu, k)}\)

\(\log(\mu) = \alpha + \beta_\mathrm{a} \cdot \mathrm{age} + \ldots\)

Model comparison

\(\mathrm{contacts} \sim \mathrm{NegBin(\mu, k)}\)

Model Δ DIC
Collective 0
Individual -5k
Covariate -50k
Covariate individual -52k

Conversational contacts

Physical contacts

Symptoms

Influenza-like illness

\(\mathrm{ili} \sim \mathrm{Binomial(1, p)}\)

Model Δ DIC
Collective 0
Collective + contacts +4
Individual +3k
Covariate -21
Covariate individual -42

ILI covariate model

\(\mathrm{ili} \sim \mathrm{Binomial(1, p)}\)

\(\mathrm{logit}(p) = \alpha + \beta_\mathrm{a} \cdot \mathrm{age} + \ldots\)

ILI

Long-term collective dynamics in contact behaviour

Age of infection of chickenpox in the UK

Hypotheses

  • Demographic change
  • Change in social mixing
  • Change in overall transmissibility

An age-structured model for long-term chickenpox dynamics

\(\beta_{ij}(t)\) varying stochastically, estimated as part of inference.

Summary & outlook

Summary

  • People are different in the amount of contact they make
  • Number of contacts appears unrelated to risk of acquiring ILI
  • Long-term changes in contact rates can be estimated by combining disease & demographic data

Acknowledgements

Ken Eames, John Edmunds

The Flusurvey and Influenzanet teams and participants

http://sbfnk.github.io